It is shown in Bonchi et al. [1]} that the functor \(\mathcal {W}\) , being
bounded, has a final coalgebra \((\Omega ,\omega )\) .
Moreover, the behavioural equivalence \(\approx _\mathcal {W}\)  coincides with \(K\) -weighted
bisimilarity \(\sim _w\) . It is also shown that \(K\) -weighted bisimilarity is
strictly included in weighted language inclusion. For completeness we
recall the proof by Bonchi et al. of the coincidence of the two relations
\(\approx _\mathcal {W}\)  and \(\sim _w\) .
